I also use the nitrile gloves, though as pointed out, they don't work well in the summer when it's really hot. The tactile issue isnt a concern for me usually. But there are some tasks that require taking them off, and I almost always get a lot of grease and crap on my arms too.
Usually I keep the Gojo soap in the shower so I can go straight from garage to shower without leaving greasy tracks everywhere, but one time I forgot that I took it out... since I was already in there, I used the liquid soap we had, which was Dr. Woods Black Soap. Man, that stuff works better than any hand cleaner I've ever used before, and it leaves your skin nice and soft afterwards.
http://www.drwoodsproducts.com/My mother-in-law gave us a couple bottles of it so we had it laying around, and now we use it for everything. Works great as a daily body-wash and face cleanser too. You can even use it as shampoo. (which is good if you have a bunch of grease in your hair!) It's something like $9.00 for a big-ass bottle of it which is pretty good since it replaces heavy-duty hand cleaner, facial cleanser, and body wash all in one.
What I like the most, is that you don't have to endure the pumice or grit of a heavy-duty cleaner on your freshly sunburned arms anymore.

Brendan
Best Hand Degreaser? This sounds daft, I was sceptical, BUT IT WORKS!
Washing up liquid and sugar. Try It!
Best Hand Degreaser? This sounds daft, I was sceptical, BUT IT WORKS!
Washing up liquid and sugar. Try It! 
Ive used washing up liquid and washing powder a few times but never sugar!
Ive never bought actual proper hand cleaner, just always use washing powder...
I have always bought the crap they sell at the local kragen, the orange stuff. Doesn't work great IMO, even with a scrub brush I find myself going crazy before I jump into the shower and I always have a haze.
A friend recently had me try dr. bronners peppermint liquid soap at the website below. I have been amazed that I can get in the shower and get wet and use this stuff with a scrub brush and get my hands clean in one sitting? I always have trouble with my damn fingernails though, but that is more of a tool issue and my stuff fingers.
http://www.drbronner.com/DBMS/PEP.htm
Dish soap or gojo with the pumice has always worked swell for me.. AS far as the gloves go, I'll pass.. I find them to be a hinderance.. Not to mention the thrill of melting them to you hand when working on a hot engine..
I use gloves about 50% of time when mechanic-ing if i'm in the nasty parts - or dealing with someone elses nasty car.
About 95% of time when painting.
That's biggest reason my hands come clean everyday.
I like the clear vinyl ones better than the blue nitrile ones.
I can get them off and back on easier - without grabbing new ones everytime.
a bargain box of no name laundry powder. You also find your cuts pretty quick.
Washing up liquid and sugar. Try It! Grin
Do yourselves a favour and try it. Detergent cuts into the grease, glycerine helps keeps your hands soft, sugar granules grind the dirt off your skin, sugar is a good antiseptic, then the whole mess dissolves in water, no gritty bits or grease.
It does sound daft though.